r the other advantage claimed for Fig.
III.--that, as it yields only particular conclusions, it is useful in
establishing contradictories against universals--for that purpose none
of its Moods can be better than Darii or Ferio.

As for Fig. IV., no particular advantage has been claimed for it. It is
of comparatively late recognition (sometimes called the 'Galenian,'
after Galen, its supposed discoverer); and its scientific claim to exist
at all is disputed. It is said to be a mere inversion of Fig. I.; which
is not true in any sense in which Figs. II. and III. may not be
condemned as partial inversions of Fig. I., and as having therefore
still less claim to recognition. It is also said to invert the order of
thought; as if thought had only one order, or as if the order of thought
had anything to do with Formal Logic. Surely, if distinction of Figure
be recognised at all, the Fourth Figure is scientifically necessary,
because it is inevitably generated by an analysis of the possible
positions of the middle term.

Sec. 10. Is Reduction necessary, however; or have not all the Figures equal
and independent validity? In one sense not only every Figure but each
Mood has independent validity: for any one capable of abstract thinking
sees its validity by direct inspection; and this is true not only of the
abstract Moods, but very frequently of particular concrete arguments.
But science aims at unifying knowledge; and after reducing all possible
arguments that form categorical syllogisms to the nineteen Moods, it is
another step in the same direction to reduce these Moods to one form.
This is the very nature of science: and, accordingly, the efforts of
some Logicians to expound separate principles of each Figure seem to be
supererogatory. Grant that they succeed; and what can the next step be,
but either to reduce these principles to the _Dictum_, or the _Dictum_
and the rest to one of these principles? Unless this can be done there
is no science of Formal Logic. If it is done, what is gained by reducing
the principles of the other Figures to the _Dictum_, instead of the
Moods of the other Figures to those of the first Figure? It may,
perhaps, be said that to show (1) that the Moods of the second, third,
and fourth Figures flow from their own principles (though, in fact,
these principles are laboriously adapted to the Moods); and (2) that
these principles may be derived from the _Dictum_, is the more
uncompromisingly gradual an